Kolmogorov-Arnold-Moser stability for conserved quantities in finite-dimensional quantum systems

Daniel Burgarth; Paolo Facchi; Hiromichi Nakazato; Saverio Pascazio; Kazuya Yuasa

doi:10.1103/PhysRevLett.126.150401

Kolmogorov-Arnold-Moser stability for conserved quantities in finite-dimensional quantum systems

Daniel Burgarth, Paolo Facchi, Hiromichi Nakazato, Saverio Pascazio, Kazuya Yuasa

ARC Centre of Excellence for Engineered Quantum Systems (EQuS)

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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Abstract

We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries, small perturbations can lead to large deviations over long times, while for robust symmetries, their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser theorem in classical mechanics. To prove this result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.

Original language	English
Article number	150401
Pages (from-to)	150401-1- 150401-6
Number of pages	6
Journal	Physical Review Letters
Volume	126
Issue number	15
DOIs	https://doi.org/10.1103/PhysRevLett.126.150401
Publication status	Published - 12 Apr 2021

Bibliographical note

Copyright 2021 American Physical Society. Firstly published in Physical Review Letters, 126(15), 150401. The original publication is available at https://doi.org/10.1103/PhysRevLett.126.150401. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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10.1103/PhysRevLett.126.150401

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Cite this

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title = "Kolmogorov-Arnold-Moser stability for conserved quantities in finite-dimensional quantum systems",

abstract = "We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries, small perturbations can lead to large deviations over long times, while for robust symmetries, their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser theorem in classical mechanics. To prove this result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.",

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AU - Pascazio, Saverio

AU - Yuasa, Kazuya

N1 - Copyright 2021 American Physical Society. Firstly published in Physical Review Letters, 126(15), 150401. The original publication is available at https://doi.org/10.1103/PhysRevLett.126.150401. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2021/4/12

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N2 - We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries, small perturbations can lead to large deviations over long times, while for robust symmetries, their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser theorem in classical mechanics. To prove this result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.

AB - We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries, small perturbations can lead to large deviations over long times, while for robust symmetries, their expectation values remain close to their initial values for all times. This is in analogy with the celebrated Kolmogorov-Arnold-Moser theorem in classical mechanics. To prove this result, we introduce a resummation of a perturbation series, which generalizes the Hamiltonian of the quantum Zeno dynamics.

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Kolmogorov-Arnold-Moser stability for conserved quantities in finite-dimensional quantum systems

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Robust Quantum Control in the Noisy Intermediate-Scale Quantum Era

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Kolmogorov-Arnold-Moser stability for conserved quantities in finite-dimensional quantum systems

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Bibliographical note

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Robust Quantum Control in the Noisy Intermediate-Scale Quantum Era

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